Pulse jet engines of a wide variety of designs have been known for over a century. Generally, they comprise a quarter wave gas resonator into which fuel and air are introduced at the pressure antinode of the resonator during the low pressure phase thereof. Some pulse jet engines include half wave resonators with power output at the pressure node or nodes.
Ignition can be achieved by the mixture of the remaining hot exhaust gases with the incoming fuel and air, so that no other ignition system is required once the engine is running.
Such an engine may be remarkably efficient for such simplicity but the noise level generated by it is totally unacceptable and cannot readily be eliminated. For this reason mainly, pulse jet engines are very seldom used.
Liquid-fuelled pulse jet engines are notoriously difficult to start but once running are extremely efficient.
More recently, there has been interest in the related pulse detonation jet engines in which a fuel/air mixture is burnt in a detonation wave front which leads to higher efficiency. However, these are not true pulse jet engines as the fuel/air mixture is introduced for each pulse which is ignited or detonated separately by a very carefully designed and controlled detonation initiator. There is no quarter wave resonance in a pulse detonation jet engine.